Dynamic Knapsack Model Report
Parameters
Model Parameters
This model is a smaller instance of the full problem:
- Planning horizon is decreased from 24 weeks to 10 weeks
- Maximum tracked wait is decreased from 6 weeks to 4 weeks
- There are 3 surgeries instead of 6 surgeries
- Number of priorities is set to 1
Simulation Parameters
- 30 Replications
- 1250 weeks duration
- 250 weeks warm up
Surgeries
- Surgery 1 - 1. SPINE POSTERIOR
DECOMPRESSION/LAMINECTOMY LUMBAR
- Surgery 4 - 4. SPINE POST CERV DECOMPRESSION AND
FUSION W INSTR
- Surgery 6 - 6. SPINE POSTERIOR DISCECTOMY
LUMBAR
Arrival Rate
It was set to be 95% of the capacity, however due to transitions, the
resource usage should be higher than 95%
| Surgery 1 |
Complexity 1 |
1.2319885 |
1.0000 |
once per week |
| Surgery 1 |
Complexity 2 |
0.6159942 |
0.5000 |
once per two weeks |
| Surgery 4 |
Complexity 1 |
0.1437320 |
0.0833 |
once per 3 months |
| Surgery 4 |
Complexity 2 |
0.1026657 |
0.0625 |
once per 4 months |
| Surgery 6 |
Complexity 1 |
1.2319885 |
1.0000 |
once per week |
| Surgery 6 |
Complexity 2 |
0.6159942 |
0.5000 |
once per 2 weeks |
Resource Usage
Usage of the resources
| Surgery 1 |
Complexity 1 |
Admissions |
0.0 |
| Surgery 1 |
Complexity 1 |
OR_Time |
3.0 |
| Surgery 1 |
Complexity 2 |
Admissions |
1.0 |
| Surgery 1 |
Complexity 2 |
OR_Time |
4.0 |
| Surgery 4 |
Complexity 1 |
Admissions |
1.0 |
| Surgery 4 |
Complexity 1 |
OR_Time |
4.0 |
| Surgery 4 |
Complexity 2 |
Admissions |
1.0 |
| Surgery 4 |
Complexity 2 |
OR_Time |
5.5 |
| Surgery 6 |
Complexity 1 |
Admissions |
0.0 |
| Surgery 6 |
Complexity 1 |
OR_Time |
1.5 |
| Surgery 6 |
Complexity 2 |
Admissions |
0.0 |
| Surgery 6 |
Complexity 2 |
OR_Time |
2.5 |
Resource Capacity
| Admissions |
1.50 |
Patients Admitted per week |
| OR_Time |
11.25 |
OR Hours per week |
R1R2 Report
This model is the default model that does not penalize bed under
utilization
Policy Description
The description will be based on the following graphs (both of them
are for M of 0 only):
The top graphs show MDP policy, and the graphs below show Myopic
policy.
The graph on the left shows in which days the policy will allow
scheduling. If the value is below 0 - the model will allow scheduling,
otherwise the model will keep patients in the waitlist. Thus this policy
will only schedule into week 1 and week 2. The plot on
the right shows the approximate priority of different surgeries. The
lower the surgery is on the list the more likely it is to be scheduled
first. The following is the order:
- Surgery 6, Complexity 2
- Surgery 6, Complexity 1
- Surgery 1, Complexity 1
- Surgery 1, Complexity 2
- Surgery 4, Complexity 1
- Surgery 4, Complexity 2
For Myopic, it is changed such that the entire horizon is filled. And
the graph on the right shows the approximate order of scheduling
priority. It appears to be very similar to MDP.
Additionally the following graphs give some insights on how the
policy makes decision

Policy Results
Wait Times in weeks
| MDP |
7.28 += 9.16 |
14.11 += 12.85 |
5.98 += 2.83 |
0.56 += 0.22 |
| myopic |
14.76 += 14.08 |
27.15 += 19.43 |
17.35 += 4.28 |
1.91 += 0.71 |
Wait List Size
| MDP |
29.25 += 7.38 |
26.73 += 7.21 |
1.49 += 0.57 |
1.03 += 0.43 |
| myopic |
58.52 += 12.2 |
50.74 += 11.84 |
4.28 += 0.94 |
3.51 += 0.73 |

Utilization
| MDP |
57.1 += 14.05 |
94.89 += 7.13 |
| myopic |
63.05 += 12.36 |
95.39 += 6.85 |
Reschedules as percentage of arrivals & Total Reschedules
| MDP |
2.6 += 0.11 |
3.6 += 0.17 |
5.4 += 0.59 |
1.22 += 0.08 |
| myopic |
12.74 += 0.33 |
14.9 += 0.41 |
71.39 += 4.52 |
2.78 += 0.17 |
Transitions per week
| MDP |
1.14 += 0.09 |
0.93 += 0.09 |
10.78 += 0.87 |
0.08 += 0.02 |
| myopic |
8.61 += 0.33 |
10.46 += 0.37 |
40.83 += 2.19 |
2.46 += 0.15 |
R1R2R3 Report
In addition to the parameters above, this model penalizes bed under
utilization in the first period
Policy Description
Additionally the following graphs give some insights on how the
policy makes decision

Policy Results
Wait Times in weeks
| MDP |
8.93 += 4.26 |
14.2 += 4.6 |
8.99 += 6.9 |
3.61 += 2.01 |
| myopic |
26.21 += 21.96 |
19.35 += 6.34 |
109.81 += 71.79 |
22.01 += 13.38 |
Wait List Size
| MDP |
35.45 += 4.62 |
26.46 += 3.58 |
2.24 += 1.04 |
6.75 += 2.07 |
| myopic |
103.97 += 22.92 |
36.02 += 7.34 |
27.3 += 10.22 |
40.66 += 9.13 |

Utilization
| MDP |
116.56 += 12.66 |
103.03 += 10.79 |
| myopic |
120.18 += 12.61 |
100.18 += 6.88 |
Reschedules as percentage of arrivals & Total Reschedules
| MDP |
65.78 += 0.65 |
59.42 += 1.63 |
0 += NA |
80.88 += 2.46 |
| myopic |
80.44 += 3.39 |
37.64 += 6.73 |
0 += NA |
134.34 += 12.61 |
Transitions per week
| MDP |
24.67 += 0.3 |
48.87 += 0.61 |
0.2 += 0.1 |
3.52 += 0.19 |
| myopic |
31.41 += 2.06 |
55.86 += 3.78 |
7.61 += 1.12 |
9.91 += 0.52 |